Analysis of integrated IDFT and Zadoff–Chu matrix precoding processes in OFDM systems

Peak signal reduction is a critical problem in orthogonal frequency-division multiplexing (OFDM) systems. Herein, we focus on Zadoff–Chu matrix (ZCM) precoding as a peak signal reduction method and analyze its integration using the discrete Fourier transform process. The analysis reveals that the integrated process can be substituted by a sparse matrix multiplication and the influence of ZCM parameters on the sparse matrix is mathematically clarified. The results also show that the ZCM precoding works to produce a single-carrier signal and explains how the ZCM precoding reduces the peak of the OFDM signal.